In order to get to Taganga, first we had to take cab to the bus station of Cartagena, located in the new city, 15 minutes away from our hostel. The ride shouldn't cost you more than 10 000 pesos. Once there you will buy a ticket to Santa Marta for approx 18 000 pesos. The bus ride is 4 hours long to get to Santa Marta. The mini-bus is confortable, with A/C on. Do not expect top quality buses, but enough to spend 4 hours seating.
The bus will make a first stop in Barranquilla, DO NOT GET DOWN HERE, if you are going to Santa Marta, there is another hour and a half bus ride before getting to the city. Once in Santa Marta, the bus will stop buy a mall. From there we got a cab for 15 000 pesos to get us to Taganga.
Gate to gate it took us 6 hours to get from Cartagena to Taganga, which is alright according to the distance, and Colombian traffic.
In Taganga booked 4 nights in a really simple hostel called Casa Mandela, on the highlands of Taganga, 5 minutes away from the beach, with A/C and breakfast included, for a decent price ( we have paid less than 100 000 pesos for the whole stay).
There is not much to do in Taganga: from there you can hike to Playa Grande, located 15 minutes away, behind the cliffs. You can also take boat trips to la playa de cristal in Tayrona Park for 80 000 pesos.
For us, we went to Taganga in order to get our Open Diver Certification, also known as the PADI (scuba diving). Later that day we went to the school we were in contact with in order to register and start the next day.